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An Efficient Numerical Scheme for Solving Multiorder Tempered Fractional Differential Equations via Operational Matrix

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  • Abiodun Ezekiel Owoyemi
  • Chang Phang
  • Yoke Teng Toh

Abstract

In this paper, we extend the operational matrix method to solve the tempered fractional differential equation, via shifted Legendre polynomial. Although the operational matrix method is widely used in solving various fractional calculus problems, it is yet to apply in solving fractional differential equations defined in the tempered fractional derivatives. We first derive the analytical expression for tempered fractional derivative for xp, hence, using it to derive the new operational matrix of fractional derivative. By using a few terms of shifted Legendre polynomial and via collocation scheme, we were able to obtain a good approximation for the solution of the multiorder tempered fractional differential equation. We illustrate it using some numerical examples.

Suggested Citation

  • Abiodun Ezekiel Owoyemi & Chang Phang & Yoke Teng Toh, 2022. "An Efficient Numerical Scheme for Solving Multiorder Tempered Fractional Differential Equations via Operational Matrix," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:7628592
    DOI: 10.1155/2022/7628592
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    References listed on IDEAS

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    1. Meng, Zhijun & Yi, Mingxu & Huang, Jun & Song, Lei, 2018. "Numerical solutions of nonlinear fractional differential equations by alternative Legendre polynomials," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 454-464.
    2. Farah Suraya Md Nasrudin & Chang Phang, 2022. "Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    3. Farah Suraya Md Nasrudin & Chang Phang & Stanislaw Migorski, 2022. "Numerical Solution via Operational Matrix for Solving Prabhakar Fractional Differential Equations," Journal of Mathematics, Hindawi, vol. 2022, pages 1-7, May.
    4. Muhammad Naeem & Hadi Rezazadeh & Ahmed A. Khammash & Rasool Shah & Shamsullah Zaland & Melike Kaplan, 2022. "Analysis of the Fuzzy Fractional-Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo-Fabrizio Derivative," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, March.
    5. Muhammad Naeem & Hadi Rezazadeh & Ahmed A. Khammash & Rasool Shah & Shamsullah Zaland, 2022. "Analysis of the Fuzzy Fractional‐Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo‐Fabrizio Derivative," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
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